Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T04:43:24.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Velocity correlations in two-dimensional electrostatic turbulence in low-β plasmas

Published online by Cambridge University Press:  13 March 2009

H. L. Pécseli  and
J. Trulsen
H. L. Pécseli
Affiliation:
University of Oslo, Institute of Physics, Box 1048 Blindern, N-0316 Oslo, Norway
J. Trulsen
Affiliation:
University of Oslo, Institute of Theoretical Astrophysics, Box 1029 Blindern, N-0315 Oslo, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

The Eulerian and Lagrangian correlation functions in low-frequency electrostatic turbulence in strongly magnetized plasmas are studied in two spatial dimensions. In this limit the ion velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E × B/B2 velocity. For strictly flute-type fluctuations, a similar model is also used for the electron dynamics. Allowing, on the other hand, for a small B-parallel component of the perturbations, an isothermal Boltzmann distribution for the electrons can be justified while the two-dimensional ion description is retained. The present analysis is based on an approximation of the actual two-dimensional flow in terms of an autonomous system consisting of many overlapping and mutually convecting vortices. Simple analytical expressions for the full space—time-varying Eulerian correlation are derived solely in terms of plasma parameters. it is demonstrated that an extension of the arguments giving the foregoing results also allows for derivation of analytical expressions for the Lagrangian correlation function. The results are supported by a Monte Carlo simulation based on the model.

Type
Research Article
Information
Journal of Plasma Physics , Volume 54 , Issue 3 , December 1995 , pp. 401 - 430
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 1977 Turbulence in Liquids. Proceedings of the 4th Biennial Symposium on Turbulence in Liquids (ed. Zakin, J. L. and Patterson, G. K.), p. 323. Science Press, Princeton.Google Scholar
Adrian, R. J. 1979 Phys. Fluids 22, 2065.CrossRefGoogle Scholar
Hasegawa, A. & Mima, K. 1978 Phys. Fluids 21, 87.CrossRefGoogle Scholar
Hasegawa, A., Imamura, T., Mima, K. & Taniuti, T. 1978 J. Phys. Soc. Jpn 45, 1005.CrossRefGoogle Scholar
Hay, J. S. & Pasquill, F. 1960 Adv. Geophys. 6, 345.CrossRefGoogle Scholar
Hesthaven, J. S., Nielsen, A. H., Pécseli, H. L. & Rasmussen, J. J. 1995 J. Atmos. Terr. Phys. 57, 215.CrossRefGoogle Scholar
Joyce, G. & Montgomery, D. 1973 J. Plasma Phys. 10, 107.CrossRefGoogle Scholar
Knorr, G., Hansen, F. R., Lynov, J. P., Pécseli, H. L. & Rasmussen, J. J. 1988 Phys.Scripta 38, 829.CrossRefGoogle Scholar
Kofoed-Hansen, O. & Wandel, C. F. 1967 Risø Report 50.Google Scholar
Kono, M. & Horton, W. 1991 Phys. Fluids B 3, 3255.CrossRefGoogle Scholar
Lynov, J. P., Nielsen, A. H., Pécseli, H. L. & Rasmussen, J. J. 1991 J. Fluid Mech. 224, 485.CrossRefGoogle Scholar
McComb, W. D. 1990 The Physics of Fluid Turbulence. Clarendon Press, Oxford.CrossRefGoogle Scholar
Misguich, J., Balescu, R., Pécseli, H. L., Mikkelsen, T., Larsen, S. E. & Qiu, Xiaoming 1987 Plasma Phys. Contr. Fusion 29, 825.CrossRefGoogle Scholar
Montgomery, D. 1975 Plasma Physics/Physique des Plasmas. Proceedings of Les Houches Summer School, Session XXII, 1972 (ed. DeWitt, C. & Peyraud, J.). Gordon and Breach, New York.Google Scholar
Montgomery, D. & Joyce, G. 1974 Phys. Fluids 17, 1139.CrossRefGoogle Scholar
Morikawa, G. K. 1960 J. Meteorol. 17, 148.2.0.CO;2>CrossRefGoogle Scholar
Novikov, E. A. 1975 Soviet Phys. JETP 41, 937.Google Scholar
Onsager, L. 1949 Suppl. Nuovo Cim. 6, 279.CrossRefGoogle Scholar
Orszag, S. A. 1969 Proceedings of the Symposium on Turbulence in Fluids and Plasmas (ed. Fox, J.), p. 17. Polytechnic, New York.Google Scholar
Panofsky, H. A. & Dutton, J. A. 1984 Atmospheric Turbulence. Wiley, New York.Google Scholar
Papoulis, A. 1984 Probability, Random Variables and Stochastic Processes, 2nd edn.McGraw-Hill, New York.Google Scholar
Pécseli, H. L. & Mikkelsen, T. 1985 J. Plasma Phys. 34, 77.CrossRefGoogle Scholar
Pécseli, H. L. & Mikkelsen, T. 1986 Plasma Phys. Contr. Fusion 28, 1025.CrossRefGoogle Scholar
Pécseli, H. L. & Trulsen, J. 1991 a Phys. Fluids B 3, 3271.CrossRefGoogle Scholar
Pécseli, H. L. & Trulsen, J. 1991 b Physica Scripta 43, 503.CrossRefGoogle Scholar
Rice, S. O. 1944 Bell Syst. Tech. J. 23, 282 (reprinted in Wax, 1954).CrossRefGoogle Scholar
Rice, S. O. 1945 Bell Syst. Tech. J. 24, 46 (reprinted in Wax, 1954).CrossRefGoogle Scholar
Sulem, C. & Sulem, P. L. 1983 J. Me'c. Theor. Appl. Numéro Special, 217.Google Scholar
Sulem, C., Sulem, P. L. & Frisch, H. 1983 J. Comp. Phys. 50, 138.CrossRefGoogle Scholar
Taylor, J. B. & McNamara, B. 1971 Phys. Fluids 14, 1492.CrossRefGoogle Scholar
Taylor, J. B. & Thompson, W. B. 1973 Phys. Fluids 16, 111.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press, Cambridge, MA.CrossRefGoogle Scholar
Wandel, C. F. & Kofoed-Hansen, O. 1962 J. Geophys. Res. 67, 3089.CrossRefGoogle Scholar
Wax, N. (ed.) 1954 Selected Papers on Noise and Stochastic Processes. Dover, New York.Google Scholar